JP7625813B2 - Estimation device, estimation method, and computer program - Google Patents

Description

The present invention relates to an estimation device, an estimation method, and a computer program.

In recent years, energy storage elements such as lithium-ion batteries have been used in a wide range of fields, including power sources for notebook personal computers, smartphones and other mobile devices, renewable energy storage systems, and power sources for IoT devices.

In order to make effective use of such secondary batteries, the behavior of the secondary battery at any given time is estimated. One method for estimating the behavior of a secondary battery is to apply a Kalman filter to an equivalent circuit model that represents the secondary battery using an electric circuit, and estimate the behavior of the secondary battery, such as the SOC (State Of Charge) (see, for example, Patent Document 1).

JP 2016-065828 A

However, the method disclosed in Patent Document 1 is configured to estimate behavior by focusing only on the terminal voltage of the storage element, and does not take into account thermal phenomena in the storage element. It is known that the characteristics of storage elements are strongly dependent on temperature, and conventional methods have low prediction accuracy. Furthermore, Patent Document 1 uses an equivalent circuit, and does not take into account electrochemical phenomena such as solid-liquid current, material diffusion, and electrochemical reactions that occur inside the battery. Conventionally, there has been no idea of coupling electrochemical phenomena and thermal phenomena in storage elements, making it difficult to obtain effective estimation accuracy in actual equipment.

The present invention was made in consideration of the above circumstances, and aims to provide an estimation device, estimation method, and computer program that take into account both the electrochemical and thermal phenomena of the energy storage element and can provide effective estimation accuracy in an actual device.

The estimation device includes an acquisition unit that acquires measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, and an estimation unit that inputs the acquired measurement data to a state estimator constructed to simulate the electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element.

The estimation method uses a computer to acquire measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, inputs the acquired measurement data into a state estimator configured to simulate the electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element.

The computer program causes the computer to acquire measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, input the acquired measurement data to a state estimator configured to simulate the electrochemical and thermal phenomena of the storage element, and execute a process to estimate the state of the storage element.

The above configuration takes into account both the electrochemical and thermal phenomena of the storage element, and can provide effective estimation accuracy in actual equipment.

1 is an external view of a power storage system according to an embodiment; FIG. 2 is an exploded perspective view showing a configuration example of an energy storage element. 3 is a schematic diagram showing a configuration example of a wound electrode body. FIG. FIG. 2 is a block diagram illustrating an internal configuration of an estimation device. FIG. 2 is an explanatory diagram for explaining a single particle model. FIG. 2 is an explanatory diagram for explaining a coordinate system in the Fick diffusion formula. 1 is a graph showing the equilibrium potential of a positive electrode. 1 is a graph showing the equilibrium potential of a negative electrode. 4 is a flowchart illustrating a state estimation procedure in the first embodiment. 13 is a flowchart illustrating a state estimation procedure in the second embodiment. 13 is a flowchart illustrating a state estimation procedure in the third embodiment. 13 is a flowchart illustrating a state estimation procedure in the fourth embodiment. FIG. 2 is a circuit diagram showing an example of an equivalent circuit model. 1 is a graph showing the relationship between lithium ion concentration and ion conductivity in an electrolyte solution. FIG. 13 is a schematic diagram showing an example of displaying a temperature state.

The estimation device includes an acquisition unit that acquires measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, and an estimation unit that inputs the acquired measurement data to a state estimator constructed to simulate electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element.
According to this configuration, the state of the energy storage element, which cannot be directly measured, can be estimated through the state variables obtained from the state estimator. In addition, since the state of the energy storage element is estimated taking into account both electrochemical phenomena and thermal phenomena, which are closely related to each other, it is possible to achieve effective estimation accuracy in an actual device.

In the estimation device, the parameters describing the electrochemical phenomenon may include an activation overvoltage of the storage element expressed as a function of the temperature of the storage element, and the parameters describing the thermal phenomenon may include a heat generation amount of the storage element expressed as a function of the activation overvoltage of the storage element. By using the activation overvoltage expressed as a function of temperature and the heat generation amount expressed as a function of the activation overvoltage as parameters, it becomes possible to estimate a state in which the electrochemical phenomenon and the thermal phenomenon of the storage element are coupled.

In the estimation device, the state estimator may be a nonlinear filter configured to output a state quantity related to the storage element when the measurement data is input. With this configuration, a nonlinear filter is used, so that a value closer to the true value can be calculated even when noise is present in the system or sensor.

In the estimation device, the nonlinear filter may include a particle filter, an ensemble Kalman filter, an extended Kalman filter, or an unscented Kalman filter. By using a nonlinear estimation algorithm, state estimation based on the physical mechanisms of electrochemical and thermal phenomena can be performed even in an environment with external disturbances.

In the estimation device, the state estimator may determine the time transition of each state variable using a state equation that represents the time transition of state variables including the concentration of occluded ions in the active material particles and the temperature related to the storage element, determine the likelihood of the state estimation using an observation equation that represents the relationship between the state variables and the observation quantities indicated by the measurement data, and update the estimated values of the state variables according to the likelihood of the state estimation that has been determined. With this configuration, the state of the storage element that cannot be directly observed can be estimated in a time series manner through the state variables that are successively updated. In this embodiment, ions occluded in the active material particles (i.e., ions in the solid phase) are referred to as occluded ions.

The estimation device includes an acquisition unit that acquires measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, and an estimation unit that inputs the acquired measurement data to a state estimator constructed to simulate an equivalent electrical circuit and thermal phenomenon of the storage element, and estimates the state of the storage element.
According to this configuration, the state of the energy storage element, which cannot be directly measured, can be estimated through the state variables obtained from the state estimator. In addition, since the state of the energy storage element is estimated taking into account the equivalent electric circuit and thermal phenomena that are closely related to each other, it is possible to demonstrate effective estimation accuracy in an actual device.

In the estimation device, the state estimator may include one or more equations in which a state quantity representing a characteristic of the storage element transitions over time or due to current flow, and may predict the deterioration of the storage element using an observation equation that represents the relationship between a state variable describing the state of the storage element and an observation quantity indicated by the measurement data. With this configuration, the deterioration of the storage element due to time or current flow can be estimated.

The estimation method uses a computer to acquire measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, inputs the acquired measurement data into a state estimator configured to simulate the electrochemical and thermal phenomena of the storage element, and estimates the state of the storage element.

The computer program causes the computer to acquire measurement data including the voltage of the storage element, the current flowing through the storage element, and the temperature related to the storage element, input the acquired measurement data to a state estimator configured to simulate the electrochemical and thermal phenomena of the storage element, and execute a process to estimate the state of the storage element.

Hereinafter, the present invention will be described in detail with reference to the drawings showing embodiments thereof.
(Embodiment 1)
1 is an external view of a power storage system 10 according to an embodiment. The power storage system 10 according to the embodiment includes an estimation device 100, power storage elements 200A-200E, and a storage case 300 that accommodates the estimation device 100 and the power storage elements 200A-200E. In the present embodiment, the power storage elements 200A-200E configure a power storage device 20. In the following description, when it is not necessary to distinguish between the power storage elements 200A-200E, they will also be simply referred to as power storage element 200.

The estimation device 100 is a flat circuit that is placed, for example, on the upper surface of a plurality of storage elements 200 and estimates the state of each storage element 200 at a given time. Specifically, the estimation device 100 acquires measurement data including the voltage of the storage element 200, the current flowing through the storage element 200, and the temperature related to the storage element 200, and estimates the state of the storage element 200 using a simulation model based on the acquired measurement data.

In the example of FIG. 1, the estimation device 100 is placed on the top surface of the energy storage element 200. Alternatively, the estimation device 100 may be placed on the side surface of the energy storage element 200 or on the bottom surface of the energy storage element 200. The shape of the estimation device 100 is not limited to a flat plate. Furthermore, the estimation device 100 may be a server device located away from the energy storage element 200, and may be configured to acquire the above-mentioned measurement data by communication and estimate the state of the energy storage element 200 using a simulation model based on the acquired measurement data.

The energy storage element 200 is a secondary battery such as a lithium ion secondary battery. The energy storage element 200 is used as a power source for automobiles such as electric vehicles (EVs), hybrid electric vehicles (HEVs), and plug-in hybrid electric vehicles (PHEVs), as a power source for electronic devices, and as a power source for power storage.

Figure 1 shows a battery pack in which five rectangular parallelepiped storage elements 200 are arranged in series. In the first embodiment, the number of storage elements 200 is described as five. Alternatively, the number of storage elements 200 may be one, or two or more. Furthermore, some storage elements 200 may be connected in parallel. The storage elements 200 may be secondary batteries other than lithium ion secondary batteries.

The configuration of the energy storage element 200 will be described below.
2 is an exploded perspective view showing a configuration example of the energy storage element 200. The energy storage element 200 is configured by housing a flat-shaped wound electrode body 210 and an electrolyte (not shown) in a hollow rectangular parallelepiped battery case 220. A positive electrode terminal 222A and a negative electrode terminal 223A for external connection are provided on a lid portion 221 of the battery case 220. The positive electrode terminal 222A and the negative electrode terminal 223A are electrically connected to a positive electrode collector 222B and a negative electrode collector 223B, respectively. The material of the battery case 220 is, for example, a metal material that is lightweight and has high thermal conductivity, such as aluminum.

Figure 3 is a schematic diagram showing an example of the configuration of the wound electrode body 210. The wound electrode body 210 is constructed by stacking a sheet-shaped positive electrode 211 on which a positive electrode active material layer 211A is formed and a sheet-shaped negative electrode 212 on which a negative electrode active material layer 212A is formed, with two sheet-shaped separators 213 in between, and winding them. The positive electrode 211 and the negative electrode 212 are arranged in a state where they are shifted from each other in the width direction of the sheet. At one end of the width direction of the positive electrode 211, an area where the positive electrode active material layer 211A is not formed is provided, and a positive electrode current collector 222B is joined to this area. For example, aluminum foil is used for the positive electrode current collector 222B. Similarly, at the other end of the width direction of the negative electrode 212, an area where the negative electrode active material layer 212A is not formed is provided, and a negative electrode current collector 223B is joined to this area. For example, copper foil is used for the negative electrode current collector 223B.

The positive electrode active material layer 211A includes a positive electrode active material. The positive electrode active material includes secondary particles consisting of aggregates of primary particles as active material particles. Particles of lithium metal composite oxide are used as the primary particles. The lithium metal composite oxide includes lithium, oxygen, and other elements (e.g., Mn, Ni, Co, Fe, Nb, W, P, Si, etc.). The elements other than lithium and oxygen may be one type or multiple types. The positive electrode active material layer 211A may further include a conductive assistant, a binder, etc. As the conductive assistant, for example, carbon black such as acetylene black (AB) or other carbon materials (such as graphite) are preferably used. As the binder, for example, polyvinylidene fluoride (PVDF) or the like is used.

The negative electrode active material layer 212A includes a negative electrode active material. For example, a carbon material such as graphite, hard carbon, or soft carbon is used as the negative electrode active material. The negative electrode active material layer 212A may further include a binder, a thickener, or the like. For example, styrene butadiene rubber (SBR) or the like is used as the binder. For example, carboxymethyl cellulose (CMC) or the like is used as the thickener.

The separator 213 is formed of a porous resin film. As the porous resin film, a porous resin film made of a resin such as polyethylene (PE) or polypropylene (PP) can be used. The separator may be formed of a resin film having a single layer structure, or may be formed of a resin film having a multi-layer structure of two or more layers. The separator 213 may be provided with a heat-resistant layer.

The electrolyte housed in the battery case 220 together with the wound electrode body 210 may be the same as that used in a conventional lithium ion battery. For example, an electrolyte containing a supporting salt in an organic solvent may be used. As the organic solvent, for example, aprotic solvents such as carbonates, esters, and ethers are used. As the supporting salt, for example, lithium salts such as LiPF ₆ , LiBF ₄ , and LiClO ₄ are preferably used. The electrolyte may contain various additives such as a gas generating agent, a film forming agent, a dispersing agent, and a thickening agent.

2 and 3, a rectangular lithium ion battery having a wound electrode body 210 has been described as an example of the energy storage element 200. Alternatively, the energy storage element 200 may be a lithium ion battery having a stacked electrode body, a cylindrical lithium ion battery, a laminated lithium ion battery, or the like. Furthermore, the energy storage element 200 may be an all-solid-state lithium ion battery that uses a solid electrolyte.

In the embodiment, the estimation device 100 described below acquires measurement data including the voltage, current, and temperature of the energy storage element 200, and estimates the state of the energy storage element 200 based on the acquired measurement data using a simulation model that simulates electrochemical and thermal phenomena.

Figure 4 is a block diagram explaining the internal configuration of the estimation device 100. The estimation device 100 is a dedicated or general-purpose computer including a calculation unit 101, a memory unit 102, an input unit 103, an output unit 104, etc. In the example of Figure 1, the estimation device 100 is provided on the upper surface of the power storage device 20. The estimation device 100 may be a device built into a battery element monitoring device (BMU: Battery Management Unit) of the power storage device 20, or may be a computer such as a server installed in a remote location. When the estimation device 100 is installed in a remote location, the acquired measurement data of the power storage device 20 is transmitted to the estimation device 100 by communication.

The calculation unit 101 is a calculation circuit including a CPU (Central Processing Unit), a ROM (Read Only Memory), a RAM (Random Access Memory), and the like. In the embodiment, the calculation unit 101 functions as a state estimator. The CPU included in the calculation unit 101 executes various computer programs stored in the ROM and the storage unit 102, and controls the operation of each of the above-mentioned hardware components, thereby causing the entire device to function as the estimation device of the present application. Specifically, the calculation unit 101 acquires measurement data including the voltage, current, and temperature of the energy storage element 200, and estimates the state of the energy storage element 200 based on the acquired measurement data using a state estimator that simulates electrochemical and thermal phenomena.

The calculation unit 101 is not limited to the above configuration, and may be any processing circuit or calculation circuit equipped with multiple CPUs, a multi-core CPU, a GPU (Graphics Processing Unit), a microcomputer, a volatile or non-volatile memory, etc. The calculation unit 101 may also have functions such as a timer that measures the elapsed time from when an instruction to start measurement is given to when an instruction to end measurement is given, a counter that counts numbers, and a clock that outputs date and time information.

The memory unit 102 is a storage device such as a flash memory. Various computer programs and data are stored in the memory unit 102. The computer programs stored in the memory unit 102 include, for example, a state estimation program PG for causing the calculation unit 101 to execute calculations using a simulation model. The data stored in the memory unit 102 include parameters used in the state estimation program PG, data temporarily generated by calculations by the calculation unit 101, and the like. The parameters stored in the memory unit 102 include parameters such as the volume, surface area, specific heat, and density of each storage element 200, the value of thermal conductance between adjacent storage elements 200, and the heat transfer rate to the outside. The state estimation program PG is provided, for example, by a non-transient recording medium M on which the computer program is readably recorded. The recording medium M is a portable memory such as a CD-ROM, a USB memory, or an SD (Secure Digital) card. The calculation unit 101 reads a desired computer program from the recording medium M using a reading device (not shown) and stores the read computer program in the storage unit 102. Alternatively, the computer program may be provided by communication.

The thermal conductance value used in the calculation of the temperature estimation may change due to the expansion of the energy storage element 200. For this reason, the memory unit 102 may store a table showing the relationship between the strain value measured by the strain sensor 103E described below and the thermal conductance value.

The value of the heat transfer coefficient used in the calculation of the temperature estimation may change depending on the air flow around the power storage device 20. For this reason, the memory unit 102 may store a table showing the relationship between the flow velocity value measured by the flow meter 103F described below and the value of the heat transfer coefficient. Alternatively, a calculation may be performed to calculate the heat transfer coefficient from a relational expression that holds between the Nusselt number, the Prandtl number, and the Reynolds number.

The input unit 103 has an interface for connecting various sensors. The sensors connected to the input unit 103 include a voltage sensor 103A that measures the voltage of the storage element 200, a current sensor 103B that measures the current flowing through the storage element 200, a temperature sensor 103C that measures the temperature of the storage element 200 (element temperature), and a temperature sensor 103D that measures the temperature around the storage element 200 (ambient temperature).

The voltage sensor 103A is an existing voltage sensor that measures the terminal voltage of the storage element 200 in a time series manner. The calculation unit 101 of the estimation device 100 acquires the voltage data measured by the voltage sensor 103A through the input unit 103 at any time.

The current sensor 103B is an existing sensor such as a current transformer or a Hall effect current sensor, and measures the current flowing through the storage element 200 in a time series manner. The calculation unit 101 of the estimation device 100 acquires the current data measured by the current sensor 103B through the input unit 103 at any time.

The temperature sensor 103C is an existing sensor such as a thermocouple or a thermistor, and measures the temperature (element temperature) of the energy storage element 200 in a time series. The calculation unit 101 of the estimation device 100 acquires temperature data measured by the temperature sensor 103C through the input unit 103 at any time. In this embodiment, the energy storage element 200 to be measured is a part (for example, the energy storage element 200E) of the five energy storage elements 200A to 200E included in the energy storage device 20. The energy storage element 200 to be measured may be one, or may be two to four. That is, when there are N energy storage elements 200 (N is an integer of two or more), the energy storage elements 200 to be measured are appropriately installed in the range of one to (N-1). The temperature sensor 103C is arranged on the upper surface of the energy storage element 200, for example. Alternatively, the temperature sensor 103C is arranged on the side or lower surface of the energy storage element 200.

The temperature sensor 103D is an existing sensor such as a thermocouple or a thermistor, and measures the temperature (environmental temperature) around the energy storage element 200 in a time series manner. The calculation unit 101 of the estimation device 100 acquires the temperature data measured by the temperature sensor 103D through the input unit 103 at any time.

A strain sensor 103E that detects the magnitude of strain of the energy storage element 200 may be connected to the input unit 103. The strain sensor 103E is an existing sensor that uses a strain gauge type load cell or the like. The strain sensor 103E is provided for each of the energy storage elements 200.

A flow meter 103F that measures the air flow around the power storage device 20 may be connected to the input unit 103. The flow meter 103F is an existing measuring device such as a flow meter. The flow meter 103F is installed at an appropriate location around the power storage device 20.

The output unit 104 has an interface for connecting an external device. An example of an external device is a display device (not shown) such as a liquid crystal display. Alternatively, the external device may be a terminal device (not shown) such as a computer or smartphone used by a user. The calculation unit 101 outputs the estimation result of the state of the power storage device 20 to the external device from the output unit 104. The estimation device 100 may have a notification unit such as an LED lamp or a buzzer to notify the user of the estimation result of the state of the power storage device 20.

The details of the calculation process executed by the estimation device 100 will be described below.
In the embodiment, the electrochemical phenomenon of the energy storage element 200 is described by a single particle model, and the thermal phenomenon is described by a heat transfer equation. The single particle model and the heat transfer equation are each rewritten into a state space model, and then rewritten into an augmented system equation that couples the two. The estimation device 100 estimates the state of the energy storage element 200 by solving the augmented system equation using a state estimator. Below, (A) a state space model using a single particle model, (B) a state space model using a heat transfer equation, (C) an augmented system equation, and (D) state estimation using an augmented system equation will be described in order.

(A) State space model using single particle model Fig. 5 is an explanatory diagram for explaining the single particle model. The Newman model is known as a physical model showing the charge and discharge behavior of a lithium ion battery. The Newman model considers a battery to be composed of three spatial regions, a negative electrode porous body, a separator, and a positive electrode porous body, and solves (1) solid phase potential distribution, (2) liquid phase potential distribution, (3) liquid phase concentration (lithium ion concentration) distribution, and (4) solid phase occluded lithium ion concentration of the positive electrode and negative electrode while also taking into account the charge transfer reaction resistance and equilibrium potential at the solid-liquid interface.

The main equations solved in the Newman model are the Nernst-Plank equation, the Fick diffusion equation, the charge conservation equation, the Nernst equation, the SOC-OCP equation, and the Butler-Volmer equation. Here, the Nernst-Plank equation represents the diffusion and migration of lithium ions in the electrolyte. The Fick diffusion equation represents the molecular diffusion of absorbed lithium ions in the solid phase of the active material particles. The charge conservation equation represents the electronic conduction in the active material particles. The Nernst equation and the SOC-OCP equation represent the equilibrium potential at the solid-liquid interface. SOC (State Of Charge) is an index that represents the state of charge, with full charge being 1 and full discharge being 0. OCP (Open Circuit Potential) is the equilibrium potential difference between the liquid phase and the solid phase when there is an oxidation-reduction reaction, and is usually expressed as a relative value to the reference electrode that serves as the standard.

The Newman model is the most successful physical model of lithium-ion batteries due to its physical sophistication and widespread use. However, because the calculation elements of the battery being calculated are finely divided in the direction of current flow, the calculation load is high and it is not suitable for online processing. Therefore, in the embodiment, a single-particle model that is a simplification of the Newman model is used. The single-particle model can significantly reduce the calculation load of the Newman model by assuming that the active material particles of the positive and negative electrodes are all in the same state.

The single-particle model is a group of ordinary differential equations that removes spatial differentials under appropriate assumptions from the Newman model, which is a group of partial differential equations that include spatial and time differentials, and is therefore easy to incorporate into the state space model described below. Details of the single-particle model are described, for example, in "Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior, Meng Guo, Godfrey Sikha, and Ralph E. White, Journal of The Electrochemical Society, 158 (2) 122-132 (2011)".

FIG. 6 is an explanatory diagram for explaining the coordinate system in the Fick diffusion equation. In the single particle model, the positive electrode active material particle is represented as one particle. The radius of the positive electrode active material particle is R _p (m). Typically, 0.1 μm<R _p <10 μm. The diffusion of the absorbed lithium ions is solved by the radial Fick diffusion equation in spherical coordinates. As the coordinate axis, the r _p axis is considered with the center of the sphere as the origin. The concentration of the absorbed lithium ions in the positive electrode active material particle is c _p . The dimension of c _p is mol/m ³ , and is a function of the position r and the time t. r _p =0 represents the center of the positive electrode active material particle. r _p =R _p is the outermost position of the positive electrode active material particle and represents the solid-liquid interface (i.e., the place where the charge transfer reaction occurs).

The radial Fick diffusion equation in spherical coordinates is as shown in Equation 1. _Dp is the diffusion coefficient ^m2 /s of the absorbed lithium ions in the positive electrode active material particles. _Dp may be a function of _rp or _cp , or a function of temperature T, but is expressed as a constant in the formula for simplification.

In order to calculate the diffusion of absorbed lithium ions, a difference equation in the case where the sphere is divided evenly in the radial direction is shown in Equation 2. As an example, the number of divisions is 5. In FIG. 6, the five divided points are shown as r ₁ , r ₂ , ..., r ₅ in order from the surface of the sphere. r ₁ represents the outermost surface of the sphere (i.e., the solid-liquid interface), and r ₅ represents the center of the sphere. The distance between adjacent calculation elements is Δr _p . In FIG. 6, an example is shown in which the sphere is divided evenly into five in the radial direction, but the number of divisions may be other than 5, and the sphere may be divided unevenly.

Here, c _p,i is the concentration of absorbed lithium ions in the division element i, Δc _p,i is the change in the concentration of absorbed lithium ions in the division element i, and Δt is the time step of the calculation. In Equation 2, central difference is used as the difference method. Alternatively, other difference methods such as forward difference and backward difference may be used.

At i=5, due to symmetry, equation 2 becomes:

At the outermost surface (i=1) of the positive electrode active material particle, there is inflow and outflow of absorbed lithium ions due to a charge transfer reaction. If the volume of the positive electrode is _Vp ( ^m3 ), the volume ratio of the active material particles is εs _,p , and the number of active material particles in the positive electrode is _np , then

Therefore, the total active material particle surface area S _p (m ² ) is expressed by the following equation (5).

At this time, the reaction current density I _reac (A/m ² ) on the surface of the active material particles is expressed by the following equation 6: Here, I (A) is the current flowing through the battery, and 0<I during discharge.

If the reaction valence is z and the Faraday constant is F (C/mol), the amount of absorbed lithium ions flowing in and out, J _p (mol/m ² s), is given by:

Therefore, the differential equation for the absorbed lithium ions at i = 1 is expressed by equation 8.

Similarly, the differential equation for the absorbed lithium ions for i = 2 to 5 can be summarized as follows:

By performing time differencing using the forward Euler algorithm, we obtain the following equation (10), where the subscripts k and k+1 are natural numbers that represent the time step.

So far, we have described the diffusion of absorbed lithium ions in positive electrode active material particles, but a similar formula also holds for the diffusion of absorbed lithium ions in negative electrode active material particles. However, for diffusion in negative electrode active material particles, all that is required is to change the subscript p to n and reverse the amount of absorbed lithium ions flowing in and out of the active material particle surface.

The sum of the total amount (mol) of absorbed lithium ions in the positive electrode active material particles and the total amount (mol) of absorbed lithium ions in the negative electrode active material particles is constant unless side reactions are taken into consideration. If the total amount of absorbed lithium ions charged at the beginning of production is N _tot (mol), N _tot is expressed by the following formula 11.

Since N _tot is a constant, one character can be eliminated from c _p,5 to c _p,1 and c _n,1 to c _n,5 . For example, when equation 11 is solved for c _n,5 , equation 12 is obtained.

In formula 12, c _p,1 to c _p,5 and c _n,1 to c _n,4 are state variables. To simplify the description, the coefficients of the state variables are represented as a _n5,p1 to a _n5,p5 and a _n5,n1 to a _n5,n4 , and the constant term is represented as f _n,5 , and the following formula 13 is obtained.

When the formula 10 expressing the concentration of the absorbed lithium ions in the positive electrode active material particles, an equation similar to the formula 10 expressing the concentration of the absorbed lithium ions in the negative electrode active material particles, and the formula 13 solved for c _n,5 are combined into one and written in matrix form, the following formula 14 is obtained, where u=1.

The values of each element of the matrix shown in equation 14 are given by equations 15 and 16. The values of elements that are not given values by equations 15 and 16 are zero.

Next, the observation equation will be described.
The concentration of absorbed lithium ions in the active material particles, as shown in Equation 14, etc., cannot be measured directly. The value that can be measured is, for example, the voltage between the terminals of the positive and negative electrodes. The voltage V is determined by the following formula:

Here, OCP _p (c _p,1 ) is the equilibrium potential of the positive electrode, and is a function of the occluded lithium ion concentration c _p,1 at the solid-liquid interface of the positive electrode active material particles. OCP _n (c _n,1 ) is the equilibrium potential of the negative electrode, as already described, and is a function of the occluded lithium ion concentration c _n,1 at the solid-liquid interface of the negative electrode active material particles. R _ohm is the voltage drop (ohmic overvoltage) due to the ohmic resistance at the electronic conductive portion and the ion conductive portion. R _ohm may be a function of temperature T. _{η act,p} (c _p,1 , I) is the activation overvoltage at the solid-liquid interface of the positive electrode active material particles, and is a nonlinear function of the occluded lithium ion concentration c _p,1 at the solid-liquid interface of the positive electrode active material particles, the current I, and the temperature T. η _act,n (c _n,1 , I) is the activation overvoltage at the solid-liquid interface of the negative electrode active material particles, and is a nonlinear function of the occluded lithium ion concentration c _n,1 at the solid-liquid interface of the negative electrode active material particles, the current I, and the temperature T. In other words, the observed voltage V is a complex nonlinear function of the occluded lithium ion concentration c _p,1 at the solid-liquid interface of the positive electrode active material particles, the occluded lithium ion concentration c _n,1 at the solid-liquid interface of the negative electrode active material particles, the current I, and the temperature T.

Each term on the right side of equation 17 will be explained below.
FIG. 7 is a graph showing the equilibrium potential of the positive electrode, and FIG. 8 is a graph showing the equilibrium potential of the negative electrode. The horizontal axis of FIG. 7 represents the occluded lithium ion concentration c _p,1 at the solid-liquid interface of the positive electrode active material particles, and the vertical axis represents the equilibrium potential OCP _p (c _{p,1 )} of the positive electrode. The horizontal axis of FIG. 8 represents the occluded lithium ion concentration c _n,1 at the solid-liquid interface of the negative electrode active material particles, and the vertical axis represents the equilibrium potential OCP _n (c n,1 ) of the negative electrode. The graphs of FIG. 7 and FIG. 8 show that the equilibrium potentials of the positive electrode and the negative electrode are nonlinear functions of the occluded lithium ion concentration at the solid-liquid interface. Theoretically, the equilibrium potential is also a function of temperature, but in practice, the effect of temperature may be ignored.

The ohmic resistance R _ohm (Ω) of the entire battery is expressed by equation 18.

Here, _Rs,pos represents the electronic resistance (Ω) of the solid phase of the positive electrode, Rs _,neg represents the electronic resistance (Ω) of the solid phase of the negative electrode, and R _I represents the ionic resistance (Ω) of the electrolyte. Each resistance may be determined by the shape and dimensions, the solid phase volume fraction, the degree of tortuosity, and the material properties. In many cases, the ohmic resistance may be considered to be almost unaffected by temperature, but it may also be a function of temperature.

The activation overvoltage η _act,p of the positive electrode is expressed by the Butler-Volmer equation (19).

Here, I is the current (A), S _p is the total active material particle surface area (m ² ), i _p0 is the exchange current density (A/m ² ), α is the transfer coefficient, n is the number of participating electrons, F is the Faraday constant (C/mol), η _act,p is the activation overvoltage of the positive electrode (V), R is the gas constant (J/(K·mol)), and T is the temperature (K). It is known that the exchange current density i _p0 is a function of the occluded lithium ion concentration c _p,1 at the solid-liquid interface of the positive electrode active material particles. As shown in Equation 19, the activation overvoltage η _act,p of the positive electrode is a complex nonlinear function of the occluded lithium ion concentration c _p,1 at the solid-liquid interface of the positive electrode active material particles, the current I, and the temperature T. Although a specific formula is not specified, the activation overvoltage η _act,n of the negative electrode is the same as the activation overvoltage η _act,p of the positive electrode.

Up to this point, an example of a single particle model has been described in (A), but this is merely one example. Other models may be used as long as they adequately represent the battery characteristics. If the computational load is not an issue, the Newman model may be used.

(B) State Space Model Using Heat Transfer Equation The heat transfer equation of the power storage device 20 shown in FIG.

Here, T ₁ to T ₅ , S ₁ to S ₅ , Q ₁ to Q ₅ , and h ₁ to h ₅ respectively represent the temperature (K), surface area (m ² ), heat generation amount (W), and heat transfer rate to the outside (W/m ² /K) of the energy storage elements 200A to 200E. _{k ij} represents the thermal conductance (W/K) between the i-th energy storage element 200 (for example, the energy storage element 200A) and the j-th energy storage element 200 (for example, the energy storage element 200B). ρ, C _p , and V represent the density (kg/m ³ ), specific heat (J/kg/K), and volume (m ³ ) of the energy storage element 200. In the embodiment, the density, specific heat, and volume of each energy storage element 200 are common, but the density, specific heat, and volume of each energy storage element 200 may be set individually. T ₀ represents the environmental temperature (K).

The left side of Equation 20 represents the amount of heat used to increase the temperature of the energy storage element 200. The term on the right side including the thermal conductance k _ij represents the thermal conduction based on the temperature difference between adjacent energy storage elements 200. The term on the right side including the heat transfer coefficients h ₁ to h ₅ represents the heat dissipation from the energy storage element 200 to the outside, and is a negative value when heat dissipation is occurring. The term including Q ₁ to Q ₅ represents heat generation from the energy storage device 20. Causes of heat generation include Joule heat and reaction heat due to current flow.

In the following description, parameters other than _T1 to _T5 are assumed to be constant (time-invariant). Alternatively, time changes of parameters other than _T1 to _T5 may be considered. Even if time changes of parameters other than _T1 to _T5 are considered, a similar calculation method is valid.

By rewriting the time differential in equation 20 using the time difference and rearranging it, we obtain the following equation 21.

Here, k represents a time step and is a natural number, and α is (ρC _p V/Δt) ⁻¹ .

Next, in order to express Equation 21 in a matrix form, the state vector x _T (k), vector b _T and matrix A _T are defined by Equation 22 below.

Here, _aT11 = 1 - α _{(S1h1 + k12} ), _aT22 = 1 - α ( _k12 + _k23 + _S2h2 ), _aT33 = 1 - α ( _k23 + _k34 + _S3h3 ), _aT44 = 1 - α ( _k34 + _k45 + _{S4h4 )} , _aT55 = 1 - α ( _k45 + _S5h5 ). Also, _aT12 = _aT21 = _{αk12 , aT23} = _aT32 = _αk23 , _aT34 = _aT43 = _{αk34 , aT45 = aT54 = αk45 , and} the rest are 0.

Using the discrete space state equation representation, Equation 22 can be written as: where control signal u _T ^k ==1.

The observation equation is expressed as in Equation 24. The upper right suffix t indicates transposition. More generally, a direct term is added to the right hand side, but in the case of heat transfer, the representative time is larger than the calculation time, so it can often be ignored.

In the observation equation of Equation 24, a scalar observation value y _T ^k is used. Alternatively, there may be a plurality of observation values. C _T is an observation vector (or observation matrix) having elements each representing the element temperature to be measured. For example, when measuring only the temperature of the fifth storage element 200, the observation vector is expressed as in Equation 25.

(C) Equations of the expanded system In the following, equations of the expanded system are derived by coupling a state space model derived using a single particle model of electrochemistry and a state space model derived using a heat transfer equation.

Equation 26 is obtained by adding a disturbance term to the occluded lithium ion concentration shown in equation 14. If the disturbance has a normal distribution (i.e., it is Gaussian noise), an unscented Kalman filter or an ensemble Kalman filter can be used. If the disturbance does not have a normal distribution, a particle filter can be used. The disturbance can be represented by a random number.

In the following, number 26 may be abbreviated as number 27.

When a battery module is composed of five single cells, the occluded lithium ion concentration is defined for each of the five single cells, so the state equation of the single particle model is composed of five equations as shown in Equation 28. Since it would be redundant to describe all of these equations, in the embodiment, only the single particle model of one battery is described.

By adding a disturbance term to the temperature shown in equation 23, we obtain equation 29. If the disturbance has a normal distribution (i.e., it is Gaussian noise), an unscented Kalman filter or an ensemble Kalman filter can be used. If the disturbance is not normally distributed, a particle filter can be used. The disturbance can be represented by a random number.

In the following, number 29 may be abbreviated as number 30.

The above-mentioned equations 26 and 27 deal with the concentration of absorbed lithium ions, and equations 29 and 30 deal with the temperature of the storage element 200. It is possible to calculate the two as independent variables, but in reality, the two are interrelated.

For example, electrochemical parameters related to temperature include the diffusion coefficients _Dp and _Dn of absorbed lithium ions and the activation overvoltages ηact _,p and _ηact,n of the positive and negative electrodes. The diffusion coefficient _Dp of absorbed lithium ions in the positive electrode active material particles shown in Equation 1 is a function of temperature and is set based on the results of experimental data and first-principles calculations. The same is true for the diffusion coefficient _Dn of absorbed lithium ions in the negative electrode active material particles. The activation overvoltages ηact _,p and _ηact,n of the positive and negative electrodes shown in Equation 17 are also functions of temperature, and an Arrhenius-type function for temperature such as the Butler-Volmer formula is used.

The amount of heat generated is one way of relating electrochemistry to temperature. The amount of heat generated by a battery is (current) x (overvoltage), and can be expressed as in Equation 31.

The final equation of state that combines electrochemistry and heat transfer is expressed as Equation 32.

If all terms were written, the formula would become complicated, so following convention, we use the nonlinear transformation function f in Equation 32. In Equation 32, the vector without a subscript in the lower right corner represents a vector that includes all electrochemical variables and temperature variables.

Since the observables are temperature and terminal voltage, the observation equation is expressed as shown in Equation 33.

Even in the observations, if the disturbance has a normal distribution (i.e., it is Gaussian noise), the unscented Kalman filter or the ensemble Kalman filter can be used. If the disturbance is not normally distributed, a particle filter can be used. The disturbance can be represented by random numbers.

(D) State Estimation Using Augmented System Equations The estimation device 100 according to embodiment 1 utilizes a particle filter to sequentially calculate time updates of a time series model represented by the state equation of Expression 32 and the observation equation of Expression 33, thereby estimating the state of the storage element 200.

The procedure of the process executed by the estimation device 100 will be described below.
9 is a flowchart illustrating a state estimation procedure in the embodiment 1. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S101). The calculation unit 101 may provide tentative values set in advance as initial values of the voltage and current of the energy storage element 200, and may provide the environmental temperature as an initial value of the temperature.

Next, the calculation unit 101 generates N particles for each state variable (step S102), where N is usually a number between 10 ² and 10 ⁶ .

Next, the calculation unit 101 generates random numbers corresponding to v _k for i=1, 2, . . . , N (step S103).

The calculation unit 101 updates the particle states to the particle states at the next time step by performing calculations based on Equation 34 for all N particles (step S104).

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C and 103D through the input unit 103 (step S105), and calculates particle weights _Pk ⁽ⁱ⁾ for all N particles based on the observation equation (step S106). The particle weight is the probability (likelihood) that the observation value _yk is observed when the state vector _xk of the particle i is obtained, and is described by the following equation.

The calculation unit 101 normalizes the particle weight P _k ⁽ⁱ⁾ calculated in step S106 based on the following equation (step S107).

The calculation unit 101 calculates a vector that is a weighted average of the particle weights and the state vector as an estimate by the particle filter (step S108). The calculation formula is as shown in Equation 37. This calculation provides estimates of the occluded lithium ion concentration and temperature in each storage element 200.

The calculation unit 101 determines whether or not to calculate the next time step (step S109). The calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not a preset time step has been reached. Alternatively, the calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the state of the energy storage element 200 has reached a preset state. If the next time step is not to be calculated (S109: NO), the calculation unit 101 ends the processing according to this flowchart.

When the next time step is to be calculated (S109: YES), the calculation unit 101 resamples the particles (stratified sampling) to estimate the next time step (step S110). The calculation unit 101 determines the state vector at time step k+1 by assuming that the state vector _xk ⁽ⁱ⁾ at time step k is restored and sampled in proportion to _pk ⁽ⁱ⁾ . After resampling the particles, the calculation unit 101 returns the process to step S104 and continues the calculation at the next time step k+1.

As described above, the calculation unit 101 of the estimation device 100 can estimate the absorbed lithium ion concentration and temperature of each storage element 200 at each time step. The calculation unit 101 may estimate various physical quantities in the storage element 200, such as SOC, OCP, and activation overvoltage, based on the estimated absorbed lithium ion concentration and temperature.

In the first embodiment, a configuration for estimating state variables using a particle filter has been described. A particle filter is a filter method targeted at state space models having nonlinearity and non-Gaussianity, and can be targeted at more general state space models without assuming linearity or Gaussianity. In addition, the particle filter has a relatively simple algorithm and can be easily implemented in the estimation device 100.

(Embodiment 2)
In the second embodiment, a state estimation algorithm using an ensemble Kalman filter will be described. That is, the estimation device 100 in the second embodiment uses the ensemble Kalman filter to sequentially calculate time updates of a time series model represented by the state equation of Expression 32 and the observation equation of Expression 33, and estimates the state of the energy storage element 200.

10 is a flowchart illustrating a state estimation procedure in the second embodiment. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S121). The calculation unit 101 may provide provisional values set in advance as the initial values of the voltage and current of the energy storage element 200, and may provide the environmental temperature as the initial value of the temperature. The variances of the disturbance term _vk in the state equation and the disturbance term _wk in the observation equation are defined as _Qk and _Rk , respectively.

Next, the calculation unit 101 generates N particles for each state variable (step S122), where N is usually a number between 10 ² and 10 ⁶ .

Next, the calculation unit 101 generates random numbers corresponding to _vk for i = 1, 2, ..., N (step S123). It is assumed that _vk follows a normal distribution and that the variance is known.

The calculation unit 101 updates the particle states to the particle states at the next time step by performing calculations based on equation 38 for all N particles (step S124).

The calculation unit 101 calculates the difference between the state vector of each particle (i=1, 2, ..., N) and the average value of the state vectors of all the particles (step S125), and calculates the covariance matrix _Pk of the predicted state quantity values for all the particles (step S126). The covariance matrix _Pk is expressed by Equation 39.

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C and 103D (step S127) through the input unit 103. The acquired sensor outputs provide the observed value y _k ⁱ of each particle at time step k.

The calculation unit 101 calculates the measurement error r _k ⁱ of the i-th particle at the time step k (step S128), where w _k is the observed disturbance. The measurement error r _k ⁱ is expressed by Equation 40.

The calculation unit 101 calculates the Kalman gain K _k at the time step k (step S129). The Kalman gain K _k is expressed by Equation 41.

The calculation unit 101 calculates an estimate x _k ⁽ⁱ⁾ _hat of the i-th particle (step S130). The estimate x _k ⁽ⁱ⁾ _hat is expressed by Expression 42. That is, the calculation unit 101 corrects the initial prediction value of Expression 38 using the observation error r _k ⁱ of Expression 40 and the Kalman gain K _k of Expression 41.

The calculation unit 101 calculates the average value x _k _hat of each particle (step S131). The average value x _k _hat of each particle represents a state vector estimate obtained by the ensemble Kalman filter, and is calculated by the following formula.

The estimated value (average value x _k _hat of each particle) obtained by Equation 43 includes the estimated values of the occluded lithium ion concentration and temperature of each energy storage element 200. The calculation unit 101 determines whether to calculate the next time step (step S132). The calculation unit 101 may determine whether to calculate the next time step by determining whether a preset time step has been reached. Alternatively, the calculation unit 101 may determine whether to calculate the next time step by determining whether the state of the energy storage element 200 has reached a preset state.

If the next time step is to be calculated (S132: YES), the calculation unit 101 returns the process to step S124 and executes the calculation at the next time step k+1. If the next time step is not to be calculated (S132: NO), the calculation unit 101 ends the process according to this flowchart.

The estimation device 100 in the second embodiment estimates state variables using an ensemble Kalman filter. The ensemble Kalman filter is a filter method targeted at state space models that have nonlinearity and non-Gaussianity, and can be used for more general state space models. The ensemble Kalman filter has a relatively simple algorithm and can be easily implemented in the estimation device 100.

(Embodiment 3)
In the third embodiment, a state estimation algorithm using an extended Kalman filter will be described. That is, the estimation device 100 in the third embodiment uses an extended Kalman filter to sequentially calculate time updates of a time series model represented by the state equation of Expression 32 and the observation equation of Expression 33, and estimates the state of the energy storage element 200.

11 is a flowchart for explaining the state estimation procedure in the third embodiment. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S141). The calculation unit 101 may provide provisional values set in advance as the initial values of the voltage and current of the energy storage element 200, and provide the environmental temperature as the initial value of the temperature. The variances of the disturbance term v _k in the state equation and the disturbance term w _k in the observation equation are set to Q _k and R _k , respectively. An initial variance-covariance matrix P is assumed.

The calculator 101 calculates the prior state estimate x ⁻ _k+1 _hat by the following equation (step S142).

The calculation unit 101 derives the Jacobian matrix of the nonlinear transformation f by the following procedure (step S143). For example, for a three-component vector represented by equation 45, if the nonlinear transformation f is expressed as equation 46, the Jacobian is calculated by equation 47. The calculation unit 101 may derive the Jacobian in advance and store it in the storage unit 102.

The calculation unit 101 calculates the a priori error covariance matrix P ⁻ _k+1 by the following equation (step S144): Here, the state transition matrix A _k is expressed by equation 49.

The calculation unit 101 calculates the Kalman gain g _k (step S145). The Kalman gain g _k is expressed by Equation 50. Here, c _k ^T is expressed by Equation 51.

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C and 103D through the input unit 103 (step S146). The acquired sensor outputs provide an observed value y _k at time step k.

The calculator 101 calculates the a posteriori state estimate x _k+1 —hat and the a posteriori error covariance matrix P _k by the following equations (step S147).

The estimate (post-state estimate x _k+1 _hat) obtained by Equation 52 includes an estimate of the occluded lithium ion concentration and temperature of each energy storage element 200. The calculation unit 101 determines whether or not to calculate the next time step (step S148). The calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not a preset time step has been reached. Alternatively, the calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the state of the energy storage element 200 has reached a preset state.

If the next time step is to be calculated (S148: YES), the calculation unit 101 returns the process to step S142 and executes the calculation at the next time step k+1. If the next time step is not to be calculated (S148: NO), the calculation unit 101 ends the process according to this flowchart.

The estimation device 100 in the third embodiment estimates state variables using an extended Kalman filter. The extended Kalman filter is a method that enables the application of a Kalman filter by linearly approximating a nonlinear model near a representative value such as the average value. The extended Kalman filter has a small computational load and can be realized by an inexpensive device.

(Embodiment 4)
In the fourth embodiment, a state estimation algorithm using an unscented Kalman filter will be described. That is, the estimation device 100 in the fourth embodiment uses the unscented Kalman filter to sequentially calculate time updates of a time series model represented by the state equation of Expression 32 and the observation equation of Expression 33, and estimates the state of the energy storage element 200.

12 is a flowchart for explaining the state estimation procedure in the fourth embodiment. The calculation unit 101 of the estimation device 100 provides an initial value of k=1 (step S161). The calculation unit 101 may provide provisional values set in advance as the initial values of the voltage and current of the energy storage element 200, and provide the environmental temperature as the initial value of the temperature. The variances of the disturbance term _vk in the state equation and the disturbance term _wk in the observation equation are set to _Qk and _Rk , respectively. An initial variance-covariance matrix P is assumed.

The calculation unit 101 generates calculation points called sigma points by using the estimated value x ⁻ _k obtained in a certain calculation step and the variance-covariance matrix P _k (step S162). If the (2n+1) generated sigma points are numbered as in Expression 53, the j-th sigma point (j is an integer that satisfies −n≦j≦n) is expressed as in Expression 54.

where sig(j) is a function that gives -1 when j<0, 0 when j=0, and +1 when 0<j. κ is a positive adjustment parameter.

The weight w _j of each sigma point is expressed as w _j =κ/2(n+κ) when j≠0, and as w ₀ =κ/(n+κ) when j=0.

The calculation unit 101 updates the states, prior state estimates, and prior error covariance matrix of all sigma points as follows (step S163).

After updating the prior state estimate and the prior error covariance matrix, the calculation unit 101 recalculates the sigma point using the following formula (step S164).

The calculation unit 101 updates the observed sigma point according to the following formula (step S165).

The calculation unit 101 calculates the prior observation estimated value y ⁻ _k+1 _hat by the following equation (step S166).

The calculation unit 101 calculates the covariance matrix P ⁻ _yy,k+1 of the prior observation errors by the following equation (step S167).

The calculation unit 101 calculates the covariance matrix P ⁻ _xy,k+1 of the prior state and observation errors by the following equation (step S168).

The calculation unit 101 calculates the Kalman gain g _k by the following equation (step S169).

The calculation unit 101 acquires the sensor outputs of the voltage sensor 103A, the current sensor 103B, and the temperature sensors 103C and 103D (step S170) through the input unit 103. The acquired sensor outputs provide an observation value y _k+1 at time step k+1.

The calculation unit 101 multiplies the difference between the observed value y _k+1 and the prior observed estimated value y ⁻ _k+1 _hat by the Kalman gain g _k to perform state estimation at time step k+1 (step S171).

The calculation unit 101 calculates the covariance matrix P _k+1 of the a posteriori observation errors by the following equation (step S172).

The posterior observation estimate (x _k+1 _hat) obtained by Equation 62 includes an estimate of the occluded lithium ion concentration and temperature of each energy storage element 200. The calculation unit 101 determines whether or not to calculate the next time step (step S173). The calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not a preset time step has been reached. Alternatively, the calculation unit 101 may determine whether or not to calculate the next time step by determining whether or not the state of the energy storage element 200 has reached a preset state.

If the next time step is to be calculated (S173: YES), the calculation unit 101 returns the process to step S162 and executes the calculation at the next time step k+1. If the next time step is not to be calculated (S173: NO), the calculation unit 101 ends the process according to this flowchart.

The estimation device 100 in the fourth embodiment estimates the short-circuit resistance using an unscented Kalman filter. The unscented Kalman filter sets multiple sample points called sigma points around the mean value and estimates the covariance matrix based on the statistical properties of these points. The unscented Kalman filter performs better than the extended Kalman filter in problems with strong nonlinearity.

(Embodiment 5)
In the fifth embodiment, a configuration in which the electrochemical phenomenon of the energy storage element 200 is represented by an equivalent circuit model will be described.

Figure 13 is a circuit diagram showing an example of an equivalent circuit model. The equivalent circuit model of the storage element 200 is often expressed by a combination of resistors, capacitance components, and voltage sources, for example, as shown in Figure 13.

In Fig. 13, _R0 is an ohmic resistance component, _R1 is a reaction resistance component of the positive electrode, _C1 is a capacitance component of the positive electrode, _R2 is a reaction resistance component of the negative electrode, _C2 is a capacitance component of the negative electrode, and _Eeq is an open circuit voltage (OCV). However, Fig. 13 is an example, and there is no restriction on the combination of series and parallel connections or the number and types of electric circuit elements.

It is known that the charge/discharge characteristics of the energy storage element 200, which is typified by a lithium-ion battery, are strongly affected by temperature and SOC. SOC is an abbreviation for State Of Charge, with a fully charged state being 100% and a fully discharged state being 0%. In the following, it is assumed that the open circuit voltage (OCV) is a function of the SOC, and R ₀ to R ₂ and C ₁ to C ₂ are functions of temperature. In this case, the state equation is expressed by Equation 64, and the observation equation is expressed by Equation 65.

Here, Δt is a time step, Cap is the full charge capacity (C) of the storage element 200, and u ^k =I (current).

Here, OCV(SOC) is a nonlinear function of SOC.

The equation that adds a disturbance to the state equation that represents the voltage of the equivalent circuit is expressed by number 66.

The equation of state for heat transfer with disturbance added is expressed by number 67.

Here, Q included in vector _bT of Equation 67 is the amount of heat generated, and is expressed as follows:

From these state equations and observation equations, the state equations and observation equations of the extended system similar to those of equations 32 and 33 are obtained. The subsequent calculation procedures are the same as those of embodiments 1 to 4, and the calculation unit 101 of the estimation device 100 can estimate the voltage and temperature of the storage element 200 using a particle filter, an ensemble Kalman filter, an extended Kalman file, and an unscented Kalman filter.

In the fifth embodiment, the open circuit voltage (OCV) is a function of the SOC, and _R0 to _R2 and _C1 to _C2 are functions of the temperature. Alternatively, the open circuit voltage may be a function of the SOC and the temperature, and _R0 to _R2 and _C1 to _C2 may be functions of the temperature and the SOC.

(Embodiment 6)
In the sixth embodiment, an example in which battery deterioration is further considered in the single particle model will be described. By using the estimation device 100, a more precise deterioration prediction simulation is possible even when based on limited temperature information. Specifically, by using the temperature estimated by the estimation device 100 as the temperature included in the known deterioration prediction formula, a more precise deterioration prediction is possible. In particular, in a storage battery system using a battery pack formed by connecting a plurality of single cells in series, the performance of a single cell with a large degree of deterioration has a very large effect on the performance of the entire storage battery system, so that it is very useful to perform a more precise deterioration prediction using the temperature estimation value obtained from the estimation device 100.

It is known that the degradation behavior of batteries is strongly affected by temperature. More accurate simulations can be performed by accurately taking temperature into account, but in reality, there is a limit to the observable quantities, and simulations based only on sensor measurements tend to be less accurate. By performing temperature correction using this method and making temperature information more accurate, it is possible to improve the accuracy of degradation predictions.

There are very few models that take into account electrochemical phenomena when simulating the deterioration of batteries. For example, "International Publication No. 2017/016966: Method for estimating the current open circuit voltage curve of a battery" discloses a method for deriving deterioration due to a decrease in charge carriers (so-called deterioration due to capacity imbalance) through numerical calculation. The method disclosed in this patent document has the disadvantage that it cannot be used while electricity is flowing and requires the battery to be stopped. In addition, it is known that the mechanism by which batteries deteriorate is not limited to a decrease in charge carriers (capacity imbalance), and this method is insufficient to cover a wide range of battery deterioration.

Other methods using machine learning include, for example, "JP Patent Publication No. 2019-168453: Deterioration Estimation Apparatus, Computer Program, and Deterioration Estimation Method." In this method, calculations are performed using machine learning, making it difficult to obtain physical insights and reflect them in product design.

In the sixth embodiment, a method for performing a degradation prediction simulation using the single particle model described in this specification is described based on the concept of the patent document "Patent Application No. 2019-064218: Development support device, development support method, and computer program."

There are at least four known degradation mechanisms for batteries, such as lithium-ion batteries: (1) isolation of active material particles, (2) reduction in charge carriers, (3) increase in electrical resistance, and (4) decrease in conductivity in the electrolyte. The combined contribution of these degradation mechanisms causes changes in the charge/discharge characteristics of the battery and leads to a decrease in capacity.

Temperature is a particularly important factor in determining the rate at which deterioration progresses. Therefore, precise understanding of temperature is also important from the perspective of deterioration prediction. The estimation device 100 can determine the rate at which deterioration progresses by assuming that the rate has temperature dependency based on, for example, an Arrhenius-type reaction rate equation. Alternatively, the estimation device 100 may determine the rate at which deterioration progresses based on any other function of temperature. It is known that there are two types of deterioration: time-related deterioration (sometimes called calendar deterioration), which occurs over time, and current-related deterioration, which occurs when electricity is applied, and it has been confirmed through experiments that both are functions of temperature.

The first degradation mechanism is the isolation of active material particles. Isolation of active material particles mainly occurs at the positive electrode during discharge, but it can also occur when the current is stopped or during discharge, or at the negative electrode. In embodiment 6, for simplicity, it is assumed that isolation of active material particles occurs only at the positive electrode during discharge, but it can be easily extended to other cases by similar equation expansion.

The calculation unit 101 of the estimation device 100 calculates the rate at which the isolation of the positive electrode active material particles progresses based on the time difference formula of equation 69.

In the formula 69, ε _s,p is the volume ratio of the positive electrode active material particles included in the formulas 4 to 6, 8, 10, and 15. The isolation of the positive electrode active material particles is expressed as a decrease in the volume ratio of the positive electrode active material particles. k _0,iso is a constant of the rate of the isolation of the positive electrode active material particles over time, and a function of temperature is used. The function may be, for example, an Arrhenius-type exponential function, or any other function. k _1,iso is a constant of the rate of the isolation of the positive electrode active material particles due to the current flow, and a function of temperature or current is used. _α is an arbitrary constant. In many cases, k _0,iso may be 0, but k _1,iso is a positive value and increases monotonically with temperature. In other words, when there is no current flow, the isolation of the positive electrode active material does not progress, and when there is current flow, the higher the temperature, the more likely the isolation of the positive electrode active material progresses. In addition to this, various modified examples are possible, such as the right side being an equation including ε _s,p itself, or a function of other state variables. Since a nonlinear filter is used, any formula may be used.

The second degradation mechanism is the reduction in charge carriers. The reduction in charge carriers is also called a capacity imbalance. This phenomenon occurs when the charge carriers that move between the positive and negative electrodes during charging and discharging are reduced due to side reactions on the electrode surface.

The calculation unit 101 of the estimation device 100 calculates the reduction in charge carriers based on the two equations described in equation 70.

b _n1 in Equation 70 is the same as the coefficient in Equation 16, and the current I in Equation 16 is replaced with (I + δ). δ is the rate of decrease of the charge carrier. This equation indicates that the absorbed lithium ion concentration c _n,1 at the solid-liquid interface of the negative electrode active material particles decreases due to factors other than the change in the absorbed lithium ion concentration accompanying the charging and discharging of the battery. Note that the current I flowing through the battery can take either positive or negative values, while δ is a positive value. N _tot in Equation 70 is the total amount of absorbed lithium ions in the positive and negative electrodes, and is the same as that described in Equation 11 and Equation 12.

In equation 71, k _0,imb is the rate of decrease in the concentration of absorbed lithium ions over time, and a function of temperature is used. The function may be, for example, an Arrhenius-type exponential function, or any other function. k _1,imb is a constant for the rate of increase in the concentration of absorbed lithium ions due to current flow, and a function of temperature or current is used. α _imb is an arbitrary constant. In many cases, k _0,imb and k _1,imb are positive values and increase monotonically with temperature. In addition to this, various modifications are possible, such as the right side being a function of other state variables. Since a nonlinear filter is used, any formula may be used.

The third degradation mechanism is an increase in electrical resistance. The causes of increased electrical resistance can be classified in more detail as peeling between the collector foil and the electrode, breakage of the conductive path of the conductive additive, and formation of a resistor film. These are described in the patent document "Japanese Patent Application No. 2019-064218: Development Support Device, Development Support Method, and Computer Program." The fourth degradation mechanism, a decrease in the conductivity of the electrolyte, is similar to an increase in electrical resistance and will be treated together.

The calculation unit 101 of the estimation device 100 calculates the rate at which the battery's electrical resistance increases based on the time difference formula in equation 72.

In equation 72, R _ohm is the ohmic resistance R _ohm of the entire battery included in equation 17, and I is the current I flowing through the battery included in equations 6, 8, 10, and 17. _{k 0,ohm} is a constant for the rate of increase in ohmic resistance over time, and is a function of temperature. The function may be, for example, an Arrhenius-type exponential function, or any other function. _{k 1,ohm} is a constant for the rate of increase in ohmic resistance due to current flow, and is a function of temperature or current. α is an arbitrary constant. In many cases, k _0,ohm and k _1,ohm are positive values and increase monotonically with temperature. In addition to this, various modifications are possible, such as the right side being an equation including R _ohm itself, or a function of other state variables. Any equation may be used because a nonlinear filter is used.

Equations 73 to 75 are the equations obtained by adding disturbance terms to the above equations.

Here, v _εs,p is the disturbance of the positive electrode active material particle volume ratio, v _δ is the disturbance term of the decrease rate of the occluded lithium ion concentration, and v _ohm is the disturbance term of the increase rate of the ohmic resistance. By adding Equations 73 to 75, which consider these disturbance terms, to Equation 32, in other words, by newly adding _εs,p , _Ntot , and _Rohm to the state variable vector _xk of Equation 32, it becomes possible to estimate the state taking into account the deterioration mechanism of the battery.

(Seventh embodiment)
In the seventh embodiment, a method for estimating the diffusion coefficient D _s,p of the absorbed lithium ions in the positive electrode active material particles and the diffusion coefficient D _s,n of the absorbed lithium ions in the negative electrode active material particles will be described. These values are known to be difficult to measure and to change from moment to moment as deterioration progresses, and are not easily obtained. Therefore, these diffusion coefficients may be included in the state variables for estimation.

Assuming that the diffusion coefficient of the absorbed lithium ions in the active material particles does not change with time, we formulate the time evolution equation shown in Equation 76.

v _Ds,p and v _Ds,n are disturbance terms. By adding these equations to the state variable vector x _k of Equation 32, the diffusion coefficient of the absorbed lithium ions in the active material particles can be estimated.

(Embodiment 8)
In the eighth embodiment, an embodiment in which battery deterioration is further considered in the equivalent circuit model will be described. In the sixth embodiment, a method for predicting deterioration based on a single particle model was described, but in the eighth embodiment, a method for predicting deterioration based on the equivalent circuit model described in the fifth embodiment will be described.

The calculation unit 101 of the estimation device 100 calculates the rate at which the deterioration of the equivalent circuit elements progresses based on the time difference equation of equation 77.

R ₀ in Equation 77 is the circuit constant described in Equation 64, Equation 65 and FIG. 13. _{k 0, R 0} is a constant of the rate of deterioration of R ₀ over time, and a function of temperature is used. The function may be, for example, an Arrhenius-type exponential function, or any other function. k _{1, R} 0 is a constant of the rate of deterioration of R ₀ due to current flow, and a function of temperature or current is used. α _{R 0} is an arbitrary constant. In addition to this, various modified examples are possible, such as an equation on the right side including R ₀ itself, or a function of other state variables. Since a nonlinear filter is used, any equation may be used. The same applies to constants other than R ₀ , R ₁ to C _2. Alternatively, a more complicated equivalent circuit may be specified, and R ₃ , R ₄ . . . and C ₃ , C ₄ . . . may be determined separately.

The deterioration prediction model based on the single particle model described in the sixth embodiment and the deterioration prediction model based on the equivalent circuit model described in the eighth embodiment may be used in combination. For example, the model of the decrease in the occluded lithium ions (capacity imbalance) in the sixth embodiment may be used for the deterioration of the equilibrium potential E _eq in the equivalent circuit model, and an equivalent circuit may be used for the internal resistance, and so on. They may be freely combined according to ease of use.

Equation 78 is obtained by adding a disturbance term to equation 77.

_vR0 is a disturbance term of _R0 , and the others are similar. By adding Equation 78, which considers these disturbance terms, to Equation 32, in other words, by newly adding _R0 , _R1 , _R2 , _C1 , and _C2 to the state variable vector _xk of Equation 32, it becomes possible to estimate the state taking into account the deterioration of the equivalent circuit elements of the battery.

The following describes some application examples.

(Application Example 1)
The estimation device 100 may be used to construct a digital twin of the power storage device 20. A digital twin refers to a technology that collects the state of a product that actually exists (temperature, current, voltage, etc.), the surrounding environment, the usage situation, etc. in real time and constructs a simulation model on a computer that is the same as the real state. In a digital twin, the simulation model is constantly updated based on values measured by sensors, and the same state as the real product can be reproduced on a computer in almost real time. By using this mechanism, when an abnormality occurs in the real product, it is reflected in the simulation model immediately, and by analyzing the simulation model, it is possible to identify the cause of the abnormality. Furthermore, since it is possible to know the behavior of latent variables that cannot be directly measured from the sensor value, it is possible to predict or prevent a failure before it occurs.

In addition, the estimation device 100 may generate information based on the estimation results, such as preventive maintenance such as part replacement, feedback to product development, prediction of replacement timing, timely maintenance, and suggestions for more efficient operating methods, and output the generated information from the output unit 104.

In addition, the simulation model can take over the analysis and diagnosis of failure causes that was previously performed by specialized employees, which is expected to result in cost reductions.

(Application Example 2)
The estimation device 100 may display the estimated state of the energy storage element 200 in real time in a graphical manner. FIG. 15 is a schematic diagram showing an example of display of the temperature state. In the example of FIG. 15, an example of a three-dimensional graphical display of the temperature of the outer surface of the energy storage device 20 is shown. The estimation device 100 generates a distribution diagram showing the temperature distribution every time the temperature state of each energy storage element 200 is estimated, and outputs the generated distribution diagram to the display device 150. In this way, the estimation device 100 can graphically display the temperature of the outer surface of the energy storage device 20 in real time on the display device 150. The display device 150 is connected to, for example, the output unit 104 of the estimation device 100. Alternatively, the estimation device 100 may be configured to include the display device 150.

The graphical display may be performed in response to a request from a user or in response to a request from maintenance personnel. By displaying graphically, the temperature state of the power storage device 20 can be intuitively understood and anomalies can be detected early. Alternatively, the estimation device 100 may display the estimated electrochemical state of the power storage device 20 in a graphical manner.

The embodiments disclosed herein are to be considered in all respects as illustrative and not restrictive. The scope of the present invention is defined by the claims, not by the above meaning, and is intended to include all modifications within the scope and meaning equivalent to the claims.

REFERENCE SIGNS LIST 10 Energy storage system 20 Energy storage device 100 Estimation device 101 Calculation unit 102 Storage unit 103 Input unit 103A Voltage sensor 103B Current sensor 103C Temperature sensor 103D Temperature sensor 104 Output unit 200 Energy storage element M Recording medium PG State estimation program

Claims (8)

an acquisition unit that acquires measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element;
an estimation unit that inputs the acquired measurement data into a state estimator that is configured to simulate an electrochemical phenomenon and a thermal phenomenon of the energy storage element, and estimates a state of the energy storage element ;
The state estimator
determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element;
calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data;
The estimator is configured to update estimates of the state variables depending on the likelihood of the determined state estimate . The parameters describing the electrochemical phenomenon include an activation overvoltage of the storage element expressed as a function of the temperature of the storage element;
The estimation device according to claim 1 , wherein the parameters describing the thermal phenomenon include a heat generation amount of the storage element expressed as a function of an activation overvoltage of the storage element. The estimation device according to claim 1 or 2, wherein the state estimator is a nonlinear filter configured to output a state quantity related to the energy storage element when the measurement data is input. The estimation device according to claim 3 , wherein the nonlinear filter comprises a particle filter, an ensemble Kalman filter, an extended Kalman filter, or an unscented Kalman filter. an acquisition unit that acquires measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element;
an estimation unit that inputs the acquired measurement data to a state estimator that is constructed to simulate an equivalent electric circuit and a thermal phenomenon of the energy storage element, and estimates a state of the energy storage element ;
The state estimator
determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element;
calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data;
The estimator is configured to update estimates of the state variables depending on the likelihood of the determined state estimate . The state estimator
The state quantity representing the characteristic of the energy storage element includes one or more equations in which the state quantity changes over time or due to current flow,
The estimation device according to claim 1 , further comprising: an observation equation expressing a relationship between a state variable describing a state of the storage element and an observation amount indicated by the measurement data, the observation equation expressing a relationship between the state variable describing a state of the storage element and an observation amount indicated by the measurement data, the estimation device predicting deterioration of the storage element. The computer
Acquiring measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element;
An estimation method for estimating a state of the energy storage element by inputting acquired measurement data to a state estimator configured to simulate an electrochemical phenomenon and a thermal phenomenon of the energy storage element, comprising:
The state estimator
determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element;
calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data;
The estimated values of the state variables are updated according to the likelihood of the obtained state estimation.
Estimation method . On the computer,
Acquiring measurement data including a voltage of a storage element, a current flowing through the storage element, and a temperature related to the storage element;
a computer program for executing a process of inputting the acquired measurement data to a state estimator configured to simulate an electrochemical phenomenon and a thermal phenomenon of the energy storage element, and estimating a state of the energy storage element, the computer program comprising:
The state estimator
determining a time transition of each state variable using a state equation expressing a time transition of a state variable including a concentration of occluded ions in the active material particles and a temperature related to the energy storage element;
calculating a likelihood of a state estimation using an observation equation that represents a relationship between the state variables and an observation amount indicated by the measurement data;
The estimated values of the state variables are updated according to the likelihood of the obtained state estimation.
Computer program .

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